Russia, which annexed Ukraine's Crimean Peninsula in 2014, backs a separatist, pro-Moscow insurgency in eastern Ukraine that has claimed nearly 10,000 lives.
Pavlov, better known by his nom de guerre 'Motorola', led the Sparta battalion and was a leading rebel commander.
Alexander Zakharchenko, the "prime minister" of the self-styled Donetsk People's Republic, said Ukrainian President Petro Poroshenko "has breached the ceasefire and declared war."
Pavlov was killed yesterday by a bomb placed in the lift of a building.
A fighter in the Sparta unit said Pavlov's bodyguard also died in the explosion.
"Either it's an operation staged by the Ukrainian services or it one of us," they said.
Several rebel chiefs considered to be adversaries of the separatist authorities have been killed far from the scene of fighting in car bombings and ambushes.
Pavlov, who took part in major battles against the Ukrainian forces around the Donetsk airport, survived an assassination attempt in June, according to local authorities.
All parties to the Ukraine conflict agreed to a peace deal brokered by Germany and France in February 2015, but while the so-called Minsk accords reduced the intensity of fighting, they failed to stop it.
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